/**
 * @author pschroen / https://ufo.ai/
 *
 * Based on https://github.com/gre/bezier-easing
 */

// These values are established by empiricism with tests (tradeoff: performance VS precision)
const NEWTON_ITERATIONS = 4;
const NEWTON_MIN_SLOPE = 0.001;
const SUBDIVISION_PRECISION = 0.0000001;
const SUBDIVISION_MAX_ITERATIONS = 10;

const kSplineTableSize = 11;
const kSampleStepSize = 1 / (kSplineTableSize - 1);

function A(aA1, aA2) {
    return 1 - 3 * aA2 + 3 * aA1;
}

function B(aA1, aA2) {
    return 3 * aA2 - 6 * aA1;
}

function C(aA1) {
    return 3 * aA1;
}

// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2
function calcBezier(aT, aA1, aA2) {
    return ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT;
}

// Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2
function getSlope(aT, aA1, aA2) {
    return 3 * A(aA1, aA2) * aT * aT + 2 * B(aA1, aA2) * aT + C(aA1);
}

function binarySubdivide(aX, aA, aB, mX1, mX2) {
    let currentX;
    let currentT;
    let i = 0;

    do {
        currentT = aA + (aB - aA) / 2;
        currentX = calcBezier(currentT, mX1, mX2) - aX;

        if (currentX > 0) {
            aB = currentT;
        } else {
            aA = currentT;
        }
    } while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS);

    return currentT;
}

function newtonRaphsonIterate(aX, aGuessT, mX1, mX2) {
    for (let i = 0; i < NEWTON_ITERATIONS; i++) {
        const currentSlope = getSlope(aGuessT, mX1, mX2);

        if (currentSlope === 0) {
            return aGuessT;
        }

        const currentX = calcBezier(aGuessT, mX1, mX2) - aX;
        aGuessT -= currentX / currentSlope;
    }

    return aGuessT;
}

function LinearEasing(x) {
    return x;
}

export default function bezier(mX1, mY1, mX2, mY2) {
    if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) {
        throw new Error('Bezier x values must be in [0, 1] range');
    }

    if (mX1 === mY1 && mX2 === mY2) {
        return LinearEasing;
    }

    // Precompute samples table
    const sampleValues = new Float32Array(kSplineTableSize);
    for (let i = 0; i < kSplineTableSize; i++) {
        sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
    }

    function getTForX(aX) {
        let intervalStart = 0;
        let currentSample = 1;
        const lastSample = kSplineTableSize - 1;

        for (; currentSample !== lastSample && sampleValues[currentSample] <= aX; currentSample++) {
            intervalStart += kSampleStepSize;
        }
        currentSample--;

        // Interpolate to provide an initial guess for t
        const dist = (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample]);
        const guessForT = intervalStart + dist * kSampleStepSize;

        const initialSlope = getSlope(guessForT, mX1, mX2);
        if (initialSlope >= NEWTON_MIN_SLOPE) {
            return newtonRaphsonIterate(aX, guessForT, mX1, mX2);
        } else if (initialSlope === 0) {
            return guessForT;
        } else {
            return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
        }
    }

    return function BezierEasing(x) {
        // Because JavaScript numbers are imprecise, we should guarantee the extremes are right
        if (x === 0 || x === 1) {
            return x;
        }

        return calcBezier(getTForX(x), mY1, mY2);
    };
}
